horsepower:torque relationship?
FormerVendor
Joined: Nov 2001
Posts: 3,065
Likes: 6
From: Houston, Tx.
Torque is quoted in Foot Pounds and Torque is rotational force.
If you want to calculate the linear distance that this force was applied through as you turned say a crank for one Revolution that was connected to a barrel of a 1 foot Radius it would be 2*Pi*Radius or another words 2*Pi or about 6.2831852... Feet for every Revolution.
Now if you were lifting a weight of one Pound on the cable wrapped around this drum you would be doing work of 6.2831852... Foot Pounds per Revolution or Work and you would have to supply one Foot Pound of Torque as well to lift it .
Now one Horsepower as OldSStroker said was determined to be the equivilant of 33,000 Foot Pounds of Work in one Minute.
So what RPM lifting 1 Pound for 6.2831852 Feet per revolution would actually be making one Horsepower?
Well 33,000 Ft Pnds per Min divided by 6.2831852 Ft Pnds per Rev = 5252 RPM !
So at 5252 RPM the Tq of 1 Foot Pound in my example equals 1 Horsepower at 5252 RPM.
If you want to calculate the linear distance that this force was applied through as you turned say a crank for one Revolution that was connected to a barrel of a 1 foot Radius it would be 2*Pi*Radius or another words 2*Pi or about 6.2831852... Feet for every Revolution.
Now if you were lifting a weight of one Pound on the cable wrapped around this drum you would be doing work of 6.2831852... Foot Pounds per Revolution or Work and you would have to supply one Foot Pound of Torque as well to lift it .
Now one Horsepower as OldSStroker said was determined to be the equivilant of 33,000 Foot Pounds of Work in one Minute.
So what RPM lifting 1 Pound for 6.2831852 Feet per revolution would actually be making one Horsepower?
Well 33,000 Ft Pnds per Min divided by 6.2831852 Ft Pnds per Rev = 5252 RPM !
So at 5252 RPM the Tq of 1 Foot Pound in my example equals 1 Horsepower at 5252 RPM.
TECH Enthusiast
Joined: Mar 2005
Posts: 566
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From: Dallas
Many people have trouble with calculus, so it's not a "simple mathematical formula." Physics doesn't divulge much into the mechanics of HOW equations are derived. That is where calc. comes into play.
I could turn around and say that anyone who can't design a basic op amp or doesn't know what a Laplace transform is a blubbering idiot not worthy of life.
I could turn around and say that anyone who can't design a basic op amp or doesn't know what a Laplace transform is a blubbering idiot not worthy of life.
Banned
Joined: Sep 2006
Posts: 282
Likes: 0
Originally Posted by gametech
Anyone who can't understand a SIMPLE! mathematical formula should revert back to the newbie forum. The original poster's question has been asked and answered, with a few side ventures. If anything else is required to explain this, your high school physics teacher should be drawn and quartered.
I can easily do the math and figure out the equation, but does that mean its easy to understand how it relates to real engines?? Hell no, its difficult to explain, even with all the numbers right in front of you. Hence the reason everyone explains it in a different way, some better than others.
Just chill out, not everyone can glance at the numbers and understand it 100%.
TECH Enthusiast
Joined: Dec 2003
Posts: 572
Likes: 0
From: Western WA
A few more notes.
To visualize torque, think of a torque wrench. You are tightening a bolt and you are applying X amount of force on a handle that is Y units long and creating X times Y amount of torque (twisting force) on the bolt. So if the wrench is 2 feet long, and you are pushing on the end with 20 pounds force you are twisting the bolt with 40 foot-pounds (or pounds-feet for you purists) of torque. Shorten the wrench to 1 foot and you'll have to push twice as hard. Lengthen it to 40 feet and you'll only have to apply 1 lb of force, hence the advantage of a breaker bar.
Now suppose that bolt was attached to something that was slipping so that you could keep turning the bolt as long as you applied a steady 40 ft-lb of torque on it. If you were superhuman and could spin the bolt 5252 rpm, you would be generating 40 horsepower.
Torque can be increased at the expense of speed by using gears. Put a 4WD truck in 4-LO and you can pull an extremely heavy load but not very fast. Likewise try starting off with the transmission in "2" sometime and you will notice less pulling power (torque) because the truck is in a higher gear (won't work with older trucks I hear). Living in mountainous country all my life, I think of it this way: Torque is what lets you pull a house trailer up a steep hill, but it takes horsepower to do it at 60 MPH.
As to why the 5252 and not, say, 4570? Well, that's just the scaling value that came out from the pony observation.
Incidentally, in places where they use the metric system, they use kilowatts instead, where 1 horsepower is approx. = to 3/4 kilowatt.
Hope this helps some.
To visualize torque, think of a torque wrench. You are tightening a bolt and you are applying X amount of force on a handle that is Y units long and creating X times Y amount of torque (twisting force) on the bolt. So if the wrench is 2 feet long, and you are pushing on the end with 20 pounds force you are twisting the bolt with 40 foot-pounds (or pounds-feet for you purists) of torque. Shorten the wrench to 1 foot and you'll have to push twice as hard. Lengthen it to 40 feet and you'll only have to apply 1 lb of force, hence the advantage of a breaker bar.
Now suppose that bolt was attached to something that was slipping so that you could keep turning the bolt as long as you applied a steady 40 ft-lb of torque on it. If you were superhuman and could spin the bolt 5252 rpm, you would be generating 40 horsepower.
Torque can be increased at the expense of speed by using gears. Put a 4WD truck in 4-LO and you can pull an extremely heavy load but not very fast. Likewise try starting off with the transmission in "2" sometime and you will notice less pulling power (torque) because the truck is in a higher gear (won't work with older trucks I hear). Living in mountainous country all my life, I think of it this way: Torque is what lets you pull a house trailer up a steep hill, but it takes horsepower to do it at 60 MPH.
As to why the 5252 and not, say, 4570? Well, that's just the scaling value that came out from the pony observation.
Incidentally, in places where they use the metric system, they use kilowatts instead, where 1 horsepower is approx. = to 3/4 kilowatt.
Hope this helps some.
TECH Fanatic
Joined: May 2005
Posts: 1,135
Likes: 1
From: The 'Burgh, PA
Originally Posted by racer7088
Yep that is correct but you know what I mean! 
4 * 2 = 8
2 * 4 = 8
TECH Senior Member
Joined: Apr 2002
Posts: 6,080
Likes: 17
From: So.Cal.
How the formula HP = TQ * RPM / 5252 is arrived at... From the physics definition of power (and keeping units consistent):
P [ftlb/s]
= F [lb] * v [ft/s]
= (T [ftlb] / r [ft]) * (ω [rad/s] * r [ft])
= T [ftlb] * ω [rad/s]
= T [ftlb] * (RPM [rev/min] * 2pi [rad/rev] / 60 [s/min])
Then:
P [HP]
= P [ftlb/s] / 550 [ftlb/s/HP]
= T [ftlb] * (RPM [rev/min] * 2pi [rad/rev] / 60 [s/min]) / 550 [ftlb/s/HP]
= T [tflb] * RPM [rev/min] / 5252 [ftlb.rev/min/HP/rad]
and [rad] is unitless.
P [ftlb/s]
= F [lb] * v [ft/s]
= (T [ftlb] / r [ft]) * (ω [rad/s] * r [ft])
= T [ftlb] * ω [rad/s]
= T [ftlb] * (RPM [rev/min] * 2pi [rad/rev] / 60 [s/min])
Then:
P [HP]
= P [ftlb/s] / 550 [ftlb/s/HP]
= T [ftlb] * (RPM [rev/min] * 2pi [rad/rev] / 60 [s/min]) / 550 [ftlb/s/HP]
= T [tflb] * RPM [rev/min] / 5252 [ftlb.rev/min/HP/rad]
and [rad] is unitless.
Last edited by joecar; Jan 22, 2007 at 01:30 PM.
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Torque is useless without RPM. We have a short hand notation for this combination of Torque and RPM... We call it 'HORSEPOWER'.
There actually is a good use for the torque curve. It is a very accurate representation of your volumetric efficiency... If you want more power, improve your torque curve. Want to improve your torque curve, improve your VE. Want to improve your VE, improve your airflow through the engine... Simple as that.
Shirl Dickey
There actually is a good use for the torque curve. It is a very accurate representation of your volumetric efficiency... If you want more power, improve your torque curve. Want to improve your torque curve, improve your VE. Want to improve your VE, improve your airflow through the engine... Simple as that.
Shirl Dickey
TECH Fanatic
Joined: Jun 2002
Posts: 1,979
Likes: 3
From: Upstate NY
Originally Posted by MrEracer
Torque is useless without RPM. We have a short hand notation for this combination of Torque and RPM... We call it 'HORSEPOWER'.
There actually is a good use for the torque curve. It is a very accurate representation of your volumetric efficiency... If you want more power, improve your torque curve. Want to improve your torque curve, improve your VE. Want to improve your VE, improve your airflow through the engine... Simple as that.
Shirl Dickey
There actually is a good use for the torque curve. It is a very accurate representation of your volumetric efficiency... If you want more power, improve your torque curve. Want to improve your torque curve, improve your VE. Want to improve your VE, improve your airflow through the engine... Simple as that.
Shirl Dickey
Another good use for the torque curve, or torque in general, is to accelerate a vehicle.
Torque at the drive wheels is resolved into a force couple at the contact patch and axle centerline. The force at the centerline is transferred to the chassis through the suspension linkage, and Newton takes over: F=Ma or a=F/M. Simple as that.
TECH Resident
Joined: Dec 2004
Posts: 845
Likes: 0
From: K-W, Ontario
The way it was explained to me:
Horsepower is not a force, it's a measurement.
Those who say, "torque wins races and horsepower sells cars" don't really
understand the relationship.
When comparing torque curves between two motors, the most average
torque in the area which the engine is spun is the engine that accelerates
the vehicle quicker.
Coincidently, the forumla also says HP is higher as torque becomes higher in said RPM window
Engines which are displacement limited use RPM and good breathing characteristics
to achieve high horsepower.
Horsepower is not a force, it's a measurement.
Those who say, "torque wins races and horsepower sells cars" don't really
understand the relationship.
When comparing torque curves between two motors, the most average
torque in the area which the engine is spun is the engine that accelerates
the vehicle quicker.
Coincidently, the forumla also says HP is higher as torque becomes higher in said RPM window
Engines which are displacement limited use RPM and good breathing characteristics
to achieve high horsepower.
TECH Fanatic
Joined: May 2005
Posts: 1,135
Likes: 1
From: The 'Burgh, PA
If you want to pin yourself back in the seat when you do a hole shot, you need Torque.
If you want to pin yourself back in the seat when you are already doing 150 MPH, you need Horsepower...
If you want to pin yourself back in the seat when you are already doing 150 MPH, you need Horsepower...
TECH Fanatic
Joined: Jun 2002
Posts: 1,979
Likes: 3
From: Upstate NY
Originally Posted by Stang's Bane
Torque = how hard you can twist
H.P. = how fast you can accelerate
Sound roughly right?
H.P. = how fast you can accelerate
Sound roughly right?
Physically, not really, because it's the force resulting from TORQUE at the drive wheels that causes the vehicle to accelerate. See post #32 above.
Realistically, think of HP as the "rate at which torque is applied", so if you said:
H.P. = how fast you can apply torque, you'd be closer.
"Twisting" harder and faster gets 'er done!
Remember that it's not peak torque or peak HP that causes the vehicle to accelerate best, but the area under the curve(s) in the rpm range in which the engine is operating.
Originally Posted by XxGarbSxX
... This equation came to be when someone (can't remember who) observed how much work a horse (a pony, to be specific) did over a certain period of time. ...
